# Neural Deformable Models for 3D Bi-Ventricular Heart Shape Reconstruction and Modeling from 2D Sparse Cardiac Magnetic Resonance Imaging

arXiv: https://arxiv.org/abs/2307.07693 · HTML: https://mlsanity.com/paper/2307.07693/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Builds on (most cited first, 9 of 9)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Deep Implicit Statistical Shape Models for 3D Medical Image Delineation](https://mlsanity.com/paper/2104.02847/) (2021)

## Built on by (most cited first, 9 of 9)

- [End-to-End 4D Heart Mesh Recovery Across Full-Stack and Sparse Cardiac MRI](https://mlsanity.com/paper/2509.12090/) (2025)
- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [Personalized 3D Myocardial Infarct Geometry Reconstruction from Cine MRI with Explicit Cardiac Motion Modeling](https://mlsanity.com/paper/2507.15194/) (2025)
- [Latent Interpolation Learning Using Diffusion Models for Cardiac Volume Reconstruction](https://mlsanity.com/paper/2508.13826/) (2025)
- [Learning Volumetric Neural Deformable Models to Recover 3D Regional Heart Wall Motion from Multi-Planar Tagged MRI](https://mlsanity.com/paper/2411.15233/) (2024)
- [AortaDiff: Volume-Guided Conditional Diffusion Models for Multi-Branch Aortic Surface Generation](https://mlsanity.com/paper/2507.13404/) (2025)
- [HeartFormer: Semantic-Aware Dual-Structure Transformers for 3D Four-Chamber Cardiac Point Cloud Reconstruction](https://mlsanity.com/paper/2512.00264/) (2025)
- [Personalized 4D Whole Heart Geometry Reconstruction from Cine MRI for Cardiac Digital Twins](https://mlsanity.com/paper/2507.15203/) (2025)
- [Bi-PT: Bidirectional Cross-Attention Point Transformers for Four-Chamber Heart Reconstruction from Sparse Cardiac MRI Data](https://mlsanity.com/paper/2607.06923/) (2026)

## Abstract (arXiv)

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.